2.1.3 Uses of Index Numbers — Practice Questions

Ten original multiple-choice questions on index numbers, weighting and the CPI, written to the style and difficulty of AQA Paper 3 Section A. Several are calculations.

10 questions AQA A-Level Multiple choice Model answers included

Not read the notes yet? Start with the 2.1.3 Uses of Index Numbers revision notes.

1. 1. When an index number series is constructed, the value given to the base year is

   Definition in context

   Select one answer

   A 0

   B 1

   C 10

   D 100
   Show model answer

   Answer: D (100). The base year is set to 100 by convention, and every other year is expressed relative to it. Using 100 is what makes the series easy to read: an index of 115 is immediately 15% above the base, and an index of 92 is 8% below it.

   Why the other options are wrong

   • A — An index of 0 would mean the variable had no value at all in the base year, which would make every later comparison impossible.
   • B — Setting the base to 1 gives a ratio rather than an index. It works arithmetically, but it is not the convention, and percentage changes are far harder to read off.
   • C — 10 is not used as a base for index numbers. There is nothing to attach the familiar 'above or below 100' reading to.

2. 2. Average weekly earnings in a town were £460 in 2019 and £529 in 2024. Taking 2019 as the base year, the index number for 2024 is

   Calculation

   Select one answer

   A 15

   B 69

   C 87

   D 115
   Show model answer

   Answer: D (115). An index number expresses the current value as a percentage of the base year value.
   Index = value in the current year ÷ value in the base year × 100.
   529 ÷ 460 × 100 = 115.
   An index of 115 says earnings in 2024 were 15% higher than in 2019. The index itself is 115; the percentage change is 15.

   Why the other options are wrong

   • A — 15 is the percentage change, not the index number. The two are easily confused because an index of 115 does mean a 15% rise, but the index has the base 100 built into it.
   • B — 69 is the cash rise, £529 − £460. An index is a ratio expressed against 100, not a difference in pounds.
   • C — 87 inverts the formula: 460 ÷ 529 × 100. That expresses the base year as a percentage of the current year, which would say earnings had fallen.

3. 3. A country's wage index, with 2020 as the base year, stood at 108 in 2022 and 135 in 2024. To one decimal place, the percentage change in wages between 2022 and 2024 was

   Calculation

   Select one answer

   A 20.0%

   B 25.0%

   C 27.0%

   D 35.0%
   Show model answer

   Answer: B (25.0%). Neither year is the base year, so the percentage change has to be worked out from the standard formula rather than read off the index.
   Percentage change = (new index − old index) ÷ old index × 100.
   (135 − 108) ÷ 108 × 100 = 27 ÷ 108 × 100 = 25.0%.
   A percentage change is always measured against the value you started from, which here is the 2022 index of 108, not the base of 100.

   Why the other options are wrong

   • A — 20.0% is 27 ÷ 135, dividing by the new index instead of the old one. The denominator is always the value you are measuring from.
   • C — 27.0% is the difference in index points, 135 − 108, read as though it were a percentage. Index points only equal percentages when the starting point is the base year of 100.
   • D — 35.0% reads the change straight off the base: 135 − 100. That is the rise since 2020, not the rise since 2022.

4. 4. Table 1 shows a simplified consumer basket with three categories. Weights are given out of 1,000 and each price index is measured against the same base year.
   Using Table 1, the weighted price index for the basket is

   Data interpretation

   Table 1: Weights and price indices for a simplified basket

   Category	Weight	Price index
   Housing	400	105
   Food	300	112
   Transport	300	108
   Total	1,000	—

   Select one answer

   A 105.0

   B 108.0

   C 108.3

   D 108.7
   Show model answer

   Answer: B (108.0). Multiply each price index by its weight, add the results, then divide by the total weight.
   Housing: 400 × 105 = 42,000.
   Food: 300 × 112 = 33,600.
   Transport: 300 × 108 = 32,400.
   Total = 42,000 + 33,600 + 32,400 = 108,000.
   Weighted index = 108,000 ÷ 1,000 = 108.0.
   The answer sits below the simple average because the largest category, housing, has the smallest price rise and pulls the index towards itself.

   Why the other options are wrong

   • A — 105.0 is the housing index on its own. Housing carries the largest weight, but the other 600 parts of the basket still count.
   • C — 108.3 is the simple average of the three indices, (105 + 112 + 108) ÷ 3. That treats a category households spend 40% of their money on exactly like one they spend 30% on, which is the whole point weights exist to avoid.
   • D — 108.7 attaches the weights to the wrong categories, putting the largest weight of 400 on the largest price rise of 112.

5. 5. A 10% rise in the price of rent has a much larger effect on the CPI than a 10% rise in the price of postage stamps. This is because rent

   Applied reasoning

   Select one answer

   A Is given a larger weight in the basket.

   B Is included in the CPI, whereas postage stamps are not.

   C Is measured more frequently than other prices in the basket.

   D Rises in price more often than other items in the basket.
   Show model answer

   Answer: A (Is given a larger weight in the basket.). The CPI is a weighted price index. Each item's price index is multiplied by a weight based on the share of household spending it accounts for, so items households spend heavily on move the overall index far more. Households spend a large fraction of income on rent and a tiny fraction on stamps, so the same percentage rise has a much bigger effect through rent.

   Why the other options are wrong

   • B — The basket contains around 700 items chosen to represent typical household spending, and both would sit inside it. The difference is the weight attached, not inclusion.
   • C — Prices across the basket are collected on the same monthly cycle. Frequency of collection is not what gives an item its influence on the index.
   • D — How often a price changes is not what weighting captures. A frequently changing price with a tiny weight still barely moves the index.

6. 6. A country's annual rate of inflation falls from 4.2% to 1.8%. It follows that

   Applied reasoning

   Select one answer

   A Prices are falling on average.

   B The CPI has fallen below 100.

   C The economy is in deflation.

   D The price level is still rising.
   Show model answer

   Answer: D (The price level is still rising.). The inflation rate is the rate at which the price level rises. At 1.8% it is still positive, so prices are still going up — just more slowly than before. A falling but positive inflation rate is called disinflation.

   Why the other options are wrong

   • A — Falling inflation is not falling prices. Prices only fall on average when the inflation rate turns negative.
   • B — The CPI is still rising, so it cannot be moving below 100. A CPI below 100 would mean prices had fallen below their base-year level.
   • C — Deflation means a negative inflation rate. At 1.8% inflation is positive, so this is disinflation, which is the confusion the two terms exist to separate.

7. 7. Table 1 shows a country's Consumer Prices Index over five years.
   Using Table 1, the year in which the rate of inflation was highest was

   Data interpretation

   Table 1: Consumer Prices Index, 2017 = 100

   Year	CPI
   2017 (base)	100.0
   2018	107.0
   2019	114.0
   2020	121.5
   2021	126.0

   Select one answer

   A 2018

   B 2019

   C 2020

   D 2021
   Show model answer

   Answer: A (2018). The inflation rate is the percentage change in the CPI over the year, so each year has to be measured against the year before it.
   2018: (107.0 − 100.0) ÷ 100.0 × 100 = 7.00%.
   2019: (114.0 − 107.0) ÷ 107.0 × 100 = 6.54%.
   2020: (121.5 − 114.0) ÷ 114.0 × 100 = 6.58%.
   2021: (126.0 − 121.5) ÷ 121.5 × 100 = 3.70%.
   The highest rate is 2018, even though it is not the year with the largest rise in index points and not the year with the highest price level.

   Why the other options are wrong

   • B — 2019 saw the same 7.0-point rise as 2018, which invites the conclusion that inflation was the same. It was not: the same rise measured against a larger starting index of 107.0 gives a smaller percentage, 6.54%.
   • C — 2020 has the largest rise in index points, 7.5. Points are not percentages — against a starting index of 114.0 that is only 6.58%.
   • D — 2021 has the highest price level, at 126.0. A high index means prices are high relative to the base year, not that they are rising quickly; 2021 in fact has the lowest inflation rate of the four.

8. 8. A country's Consumer Prices Index was 124.0 last year and is 129.0 this year. To one decimal place, the rate of inflation is

   Calculation

   Select one answer

   A 3.9%

   B 4.0%

   C 5.0%

   D 29.0%
   Show model answer

   Answer: B (4.0%). The inflation rate is the annual percentage change in the CPI.
   (CPI this year − CPI last year) ÷ CPI last year × 100.
   (129.0 − 124.0) ÷ 124.0 × 100 = 5.0 ÷ 124.0 × 100 = 4.0%.
   The change is measured against last year's index of 124.0, because that is the level prices are rising from.

   Why the other options are wrong

   • A — 3.9% divides by this year's index: 5.0 ÷ 129.0. A percentage change is always measured against the original value, not the new one.
   • C — 5.0% is the change in index points, 129.0 − 124.0, read as a percentage. Those only coincide when the starting index is 100.
   • D — 29.0% reads the change against the base year: 129.0 − 100. That is the total rise in prices since the base year, not this year's inflation rate.

9. 9. A country's labour productivity index, with 2015 as the base year, stood at 112 in 2024. This tells us that productivity in 2024 was

   Applied reasoning

   Select one answer

   A 12% higher than in 2015.

   B 12% lower than in 2015.

   C 112% higher than in 2015.

   D Unchanged since 2015.
   Show model answer

   Answer: A (12% higher than in 2015.). The base year is 100, so an index of 112 is 12 above the base. Because the comparison is with the base year itself, the percentage change can be read straight off: productivity was 12% higher in 2024 than in 2015. This direct reading only works against the base year.

   Why the other options are wrong

   • B — An index above 100 means the variable has risen since the base year. Below 100 would mean a fall.
   • C — 112% higher would mean productivity had more than doubled. The index is 112, but the percentage change is the amount above 100, which is 12.
   • D — Unchanged would show as an index of exactly 100. Any departure from 100 is a change relative to the base year.

10. 10. Two countries each report a house price index of 130, both using 2019 as the base year. All other things being equal, it follows that

    Applied reasoning

    Select one answer

    A Both countries use the same basket of houses in their index.

    B House prices are now at the same level in both countries.

    C House prices have risen by 30% in each country since 2019.

    D House prices rose faster in the country with the higher average price.
    Show model answer

    Answer: C (House prices have risen by 30% in each country since 2019.). An index number measures change relative to its own base year, and nothing else. Both indices are 130 against a base of 100, so house prices in each country are 30% above their own 2019 level. That is the only comparison the two numbers support.

    Why the other options are wrong

    • A — Each country builds its own index from its own housing market. Identical index values say the two markets moved by the same proportion, not that they measure the same thing.
    • B — This is the classic misreading: an index shows change, not level. One country's houses could average £150,000 and the other's £400,000 and both indices would still read 130.
    • D — Both rose by the same 30%, whatever the price levels behind them. The index carries no information about which country's houses cost more.